Lithium secondary batteries (and typically, lithium ion batteries), which charge and discharge due to migration of lithium ions between a positive electrode and a negative electrode, are expected to continue to increase in demand in the future for use as vehicle-mounted power supplies or as power supplies of personal computers and portable devices because they are lightweight and allow the obtaining of high energy density. In a typical configuration of this type of secondary battery, an electrode is provided having a configuration in which a material capable of reversibly storing and releasing lithium ions (electrode active material) is retained in an electrically conductive member (electrode current collector). An example of an electrode active material used in a positive electrode (positive electrode active material) is a so-called olivine-type lithium manganese phosphate compound (such as LiMnPO4) that contains lithium. Since olivine-type lithium manganese phosphate compounds have a high theoretical capacity, are inexpensive and have superior stability, they are attracting attention as a promising positive electrode active material. Examples of the prior art relating to this type of positive electrode active material include that described in Patent Documents 1 and 2.    Patent Document 1: Japanese Patent Application Laid-open No. 2009-527085    Patent Document 2: Japanese Patent Application Laid-open No. 2009-120479
Production of an olivine-type lithium manganese phosphate compound as described above is carried out by using, for example, a sol-gel method. For example, Patent Document 1 describes the production of LiMnPO4 by weighing out and mixing starting raw materials consisting of a lithium compound and manganese compound at a molar ratio (namely, stoichiometric ratio) Mn/Li of 1, and then synthesizing LiMnPO4 by a sol-gel process. However, according to studies carried out by the inventor of the present application, in a lithium secondary battery that uses LiMnPO4 obtained according to such a process as a positive electrode active material, it was determined that the resulting capacity is not as high as expected.